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The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

A test used to determine the statistical significance of an observation. Two main types of error can occur: 1. A type I error occurs when a false negative result is obtained ...

The stomachion is a 14-piece dissection puzzle similar to tangrams. It is described in fragmentary manuscripts attributed to Archimedes as noted by Magnus Ausonius (310-395 ...